Speaking of which, it's supposed to be in the 60's this weekend, so the POS car will likely spend the weekend on jack stands getting the starter replaced.
Fortunately my neighbor rebuilds starters and alternators. Hopefully he's got the parts for this one.
I'm positive it's not the flywheel. I opened the hood to make sure I was really turning the engine then rocked it enough in 4th to make sure I got the engine turned about 45 degrees and it still wouldn't start. Just spins the starter.
Edit: Looking in the shop manual right now, and this doesn't look like it's going to be remotely fun. But also looks like jack stands won't help much. Looks like I'll have to get at least the radiator shroud out of the way then fumble around blind a bit.